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To convert 0.135 repeating to a fraction, we can set x = 0.135135135... and then multiply by 1000 to shift the decimal point: 1000x = 135.135135... Subtracting the original equation from this new equation gives 999x = 135. Subtracting the two equations gives 999x - x = 135 - 0.135, simplifying to 998x = 134.865. Dividing both sides by 998 gives x = 134.865/998, which simplifies to 6743/49900. Therefore, 0.135 repeating as a fraction is 6743/49900.
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